It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new mo...It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.展开更多
This paper considers the problem of optimal multi-objective trajectory design for autonomous rendezvous. Total velocity cost and relative state robustness of close-looped control are selected as the objective function...This paper considers the problem of optimal multi-objective trajectory design for autonomous rendezvous. Total velocity cost and relative state robustness of close-looped control are selected as the objective functions. Based on relative dynamics equations, the state equations and measurement equations for angles-only relative navigation between spacecraffs are set forth. According to the method of linear covariance analysis, the close-looped control covariance of the true relative state from the reference relative state is analyzed, and the objective functions of relative state robustness are formulated. Considering the total velocity cost and the relative state robustness, the multi-objective optimization algorithm of NSGA-II is employed to solve this multi-impulsive rendezvous problem. Lastly, the validity of the objective functions and the covariance results are demonstrated through 1 00 times Monte Carlo simulation.展开更多
文摘It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.
基金supported by the National Natural Science Foundation of China (Grant No. 10902101)
文摘This paper considers the problem of optimal multi-objective trajectory design for autonomous rendezvous. Total velocity cost and relative state robustness of close-looped control are selected as the objective functions. Based on relative dynamics equations, the state equations and measurement equations for angles-only relative navigation between spacecraffs are set forth. According to the method of linear covariance analysis, the close-looped control covariance of the true relative state from the reference relative state is analyzed, and the objective functions of relative state robustness are formulated. Considering the total velocity cost and the relative state robustness, the multi-objective optimization algorithm of NSGA-II is employed to solve this multi-impulsive rendezvous problem. Lastly, the validity of the objective functions and the covariance results are demonstrated through 1 00 times Monte Carlo simulation.
